It's a common misconception that dedicated training on the parallettes will cause you to become imbalanced, lose your gains, or lose your "pulling" strength.
But that's just not true!
What a lot of people don't understand about "pushing" vs "pulling" exercises is that many of the actual movements aren't that different at the anatomical level. For example, one key component of a pull-up is the retraction and depression of the shoulder scapula, which pulls the body upward when the arms are overhead.
However, if the arms are hanging down, the same scapular depression and retraction movement becomes a "press" - look at our L-sit tutorials, and you'll see Ryan pushing his shoulders away from his ears.
It's the same as the "pulling prep" movement he demonstrates in the pull-up tutorials.
In other words, P-bar training doesn't make you weak at pulling.
If you do it the way we teach it, it will probably even improve your strength in "pulling" movements like pull-ups, though your numbers may decrease slightly in the short term, since you won't be practicing the technique.